haze around white birds -- how might I avoid it?

I'm using a Canon 70D with a Sigma 100-400 mm contemporary lens. In bright sun (and auto ISO, which can result in over exposure) I sometimes get a white haze around egrets etc, but it is worse in some photos than others.

The two (greatly cropped) shots below were taken in the same burst at 3 frames a second.

Set your camera to fully manual and lower your iso, shoot in RAW then you can change your iso levels when you edit your pics, RAW will also give you 16bits so a better quality picture, you could also try noise reduction and sharpness adjustments when editing a RAW picture, these are just some things i think you can try to help your pics,( i am by no means an expert )

I can't see the white haze you are referring to but with white birds in bright light the white is very prone to washing out, maybe some negative EV will help or if possible change your position to minimise the glare.

If your bird is static then you don't really need high shutter speeds only if the bird is moving. High shutter speeds will push your ISO up if you use auto ISO however you can set an upper limit for Auto ISO. If you use back button focusing there is plenty of info on how to set the the upper and lower limits on shutter speed and ISO.